I was visiting an excellent liberal arts college in a scenic location and my host, while showing me the athletic facilities, said, “We price it out as a luxury resort and throw in the education for free.” I’m sure it was a joke. Well, pretty sure.

Economists generally favor competition, on the ground that it usually increases efficiency and lowers costs, but there may be exceptional cases in which competition raises costs. To the extent that the competition of colleges for students takes the form of luxury-resort “extras,” competition among colleges may be such an exceptional case—a case in which competition increases cost. Climbing walls and rugby pitches are fine things, but it could be that all would be better off with fewer climbing walls and rugby pitches and cheaper tuitions.

Perhaps a different approach to matching students and colleges could make sense. We have learned a good deal about matching people and opportunities in recent decades. Some of the most important contributors to this learning, mathematician Lloyd Shapley and economist Alvin Roth, were honored by the 2012 Nobel Memorial Prize in Economic Sciences. This is not “just theory:” the deferred acceptance algorithm they studied was tested by experiment and has been put to work successfully in a number of real applications, as the Nobel committee noted. This proposal is based on their work.

The clearinghouse would, of course, be voluntary. Participating colleges would agree to some guidelines. At the outset, each college would inform the clearinghouse of its target for the number of students it would expect to recruit in this way. Each student would submit a single application to the clearinghouse, with a listing of the colleges by which the student would wish to be considered. The colleges should be ranked in order of the student’s preference, ideally from the first choice down to the least preferred college that the student would consider.

The matching would take place in stages. At the first stage, each application would be forwarded to the college listed as the student’s first preference. Each college would rank the applicants according to their own criteria and, for each application, make one of three responses: accepted, rejected or reserved, with the total of accepted and reserved no more than the college’s recruitment target. It must be understood that no application is reserved unless the college is willing to accept the student if it cannot reach its target with students it would rank more highly; others should be rejected.

At the second stage, applications rejected would be sent on to the college listed second on the student’s preference list. Each college would then rank the new applicants and revisit its reserved list and again give each student on this expanded list of reserved and new applicants one of the same three responses. Once again, applications rejected at this stage would be sent to the next college on the student’s preference list. This process would be repeated until no there are no more rejections and at that point the students on a college’s reserved list would be considered accepted.

Ideally, the outcome of this process will have an important property. To express the property, define a frustrated pair as a college A and a student B such that 1) they are not matched, 2) B would prefer A to the college he was admitted to and 3) A ranks B higher on its criteria than some students it has accepted. The property of the deferred acceptance algorithm is that, at its end, there are no frustrated pairs. This in turn means that nobody can gain by “gaming the system,” admitting poor students to fill the pool nor focusing student applications on lesser schools because the better ones seem to be a long-shot.

Perhaps, qualitatively, this is the most important result: each student would be able to aspire as high as she wishes, without sacrificing the more realistic possibilities.

Of course, nothing ever works ideally. First, if there are more students than places, some students will not be accepted; if more places than students, some colleges will not reach their enrollment targets. The review process will need to be complicated a bit to deal with this. Second, it is not to be expected that students will rank all the available colleges without ties (Unlisted colleges may be considered tied for last place). Ties might be resolved at random, but in this case broader preferences by location, tuition cost and college type will need to be taken into account in resolving ties. Still other issues are sure to arise from experience.

Nevertheless, experience shows that the ideal case of no frustrated pairs can be approximated closely in practice, and this means that both colleges and students will have good reason to participate once the clearinghouse is in place. Conversely, participation can only be voluntary. Certainly, if some of our best universities were to lead the way, the institution of such a clearinghouse would be eased and its chances for success improved. However, while even the best could gain from the no-frustrated-pairs condition, it is unlikely that they would risk a situation in which they do very well. If a broad coalition could be formed of good to very good universities, perhaps the state colleges and universities of several states, this could probably introduce the clearinghouse successfully.

Federal leadership could certainly promote the initiation and maintenance of a clearinghouse. If this were done, and (as experience suggests) the clearing house would prove successful, it would be likely to attract more participation and, perhaps, become the default approach to recruiting students, even among the elite.

The no-frustrated-pairs property is valuable, but a clearinghouse could be expected to have another advantage: it should be cheaper than unrestrained competition among colleges. Climbing walls and rugby pitches will still play a part, as colleges want to attract the first-preference listings, but conversely—to the extent that they can attract students of the quality they seek through the clearinghouse—many colleges will find that kind of competition less necessary and less useful, and will engage less in it. Some colleges, at least, can give up trying to be luxury resorts and concentrate on being excellent academic institutions. And that would be a gain all around